Emma and Winnie have some cards. If Emma gives 11 cards to Winnie, Winnie will have 5 times the number of cards as Emma. If Winnie gives 19 cards to Emma, Emma will have
25 as many cards as Winnie. How many cards does Emma have at first?
|
Case 1 |
Case 2 |
|
Emma |
Winnie |
Emma |
Winnie |
Before |
7 u + 11 |
35 u - 11 |
12 u - 19 |
30 u + 19 |
Change |
- 11 |
+ 11 |
+ 19 |
- 19 |
After |
1x7 = 7 u |
5x7 = 35 u |
2x6 = 12 u |
5x6 = 30 u |
The total number of cards in both cases remains unchanged. Make the total number of cards in both cases the same. LCM of 6 and 7 is 42.
Number of cards that Emma had at first is the same in both cases.
12 u - 19 = 7 u + 11
12 u - 7 u = 11 + 19
5 u = 30
1 u = 6
Number of cards that Emma had at first
= 7 u + 11
= 7 x 6 + 11
= 42 + 11
= 53
Answer(s): 53